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thirty-seven writes "According to four Canadian psychologists, a study they have conducted shows that math anxiety, 'the feeling of fear and dread of performing mathematical calculations,' can negatively affect mathematical tasks much simpler and more basic than previously thought. In the study, participants were asked to count black squares on a white screen. The number of squares shown ranged from one to nine and participants were given as much time as they wanted before answering. When the number of squares was in the subitizing range (one to four), both math-anxious and non-math-anxious participants performed equally well, but when the number of squares was in the counting range (five to nine), the math-anxious group took longer and were less accurate. The University of Waterloo's news release about the study includes this interesting note: 'Previous studies have shown that a weakness in basic math abilities has a greater negative effect on employment opportunities than reading difficulties [do].'"

Although Mikkeles does cover the concept, he doesn't specify that this process is called "subitizing" (as referred to TFS) and has to do with the underlying method in which the human brain interprets data. See The Discrimination of Visual Number [jstor.org], Kaufman et al.

Certainly. If you actually have a phobia of something, the smallest notion can affect you.

I don't think that math anxiety is a "phobia" for most people; it is milder and much more widespread among the general population, I think. Wikipedia (not an authoritative source for definitions of psychology terms, I know) says a phobia is "an intense and persistent fear" and that mathematical anxiety is "anxiety about one's ability to do mathematics" and anxiety is an "unpleasant feeling that is typically associated with uneasiness, fear, or worry."

Yes, you can use your watch if you're in a situation where you can use it. Let's see.. I've performed first aid while holding on to the side of a boat, in a street intersection, through a car window. One of the three times I had both hands free, and there was enough daylight to use the watch. Through the car window... I could have repositioned to use my watch.
Assuming you have a watch. Most people now use the pocketwatch which is part of their cell phone, and you might need several button presses to a

Exactly. When science (actually Galileo) tried to confirm the "obvious" notion that heavy objects fall faster, it turned out that what was everybody thought was "obvious" was wrong. Hence the need to confirm things that seem obvious at first glance with scientific observation and analysis.

It was also "obvious" that the Sun orbited the Earth until a significant amount of data supporting the heliocentric theory was found. Science requires data not just peoples' "intuition" which is very often wrong.

To add to that, if it were not for science's ability to question seemingly simple things, for all we know every time one steps on the gas pedal an invisible ectoplasm materializes and pushes our chest towards the seat of the car.

We do in fact feel a force, but because of experimentation and further exploration, we understand the fictitious force due to the nonuniform motion of two reference frames (or the acceleration of the non-inertial frame), in this case rectilinear acceleration. Intuition told us we were being pushed into the seat, but in reality, nothing is pressed against our chest.

No it is not a question of frame of reference, it is a question of models. The solar system could be modeled in infinitely many ways. The geocentric model models the routes of the other planets with "epicycles".

Which model should we use? Enter Occam's Razor. We should use the simplest. Although you could work with a geocentric model, why would you want to when the heliocentric model also describes the motions of the planets, and does so more simply and more accurately? As an example of how difficult

That point lies within the Sun its self. The degree to which geocentric theory is wrong is several orders of magnitude more than the degree to which ideal heliocentric theory is. Geocentric theory could not be extended and at the same time remain internally consistent as well as explain the orbits of various objects in space. Heliocentric theory O.T.O.H. can easily be extended by Newton and later Einstein to match observations to an extreme degree of accuracy.

I have a bachelor's degree in math, and I graduated with a 4.0 GPA. Though I realize that's not all that impressive among the Slashdot crowd, I have done math that would make most normal men weep, and I excelled at it. However, if you were to come up to me and ask me what 7*13 is, I would turn white as a sheet, stammer a bit, and, after several minutes, give you an answer that is likely incorrect. There's just something about being put on the spot like that that shifts my brain into panic mode.

In a similar vein, I participated in a few math-bowl competitions in high school. Even though I was excellent at math, I sucked in the completion. When you start into anything beyond arithmetic then there is really little point in mental math. Sure I could figure out 7*13 but when you do math with more letters than numbers, there isnt much reason to do it by hand anymore.

With chemical anxiolytics, you can substantially damp somebody's anxiety responses to things that usually scare them. With the right chemical anxiolytics, you can even do so without rendering them useless for other things.

Repeat the experiment; but have all participants(normal and anxiety groups) take a pill ~30 minutes before the questioning. Half of each group will get a placebo, half will get a milligram or two of Lorazepam. The effect of Lorazepam

"Isn't it obvious that the fear of something will have an impact even on the simplest things where something relative to that fear is involved?"

I'll say: no, not obvious. Equally legitimate suppositions:(1) It is the difficulty of the task which "will have an impact" on people's emotional state, not the other way around.(2) People's fear reactions should make them more focused, attentive, and capable.

Isn't it obvious that the fear of something will have an impact even on the simplest things where something relative to that fear is involved ?

I don't think it's math anxiety that caused these results. I think it's anxiety in general.

I took part in a psych study about a decade ago (conveniently at the U of Waterloo) for a similar thing. I was asked to count arcs -- line-drawn half-circles, pointed in an upwards or downwards direction placed randomly on a screen. There would be somewhere between 5 to 15 of these on the screen, and instructions were to count all the "upward arcs" or "downward arcs" as fast as possible. After a few trials, I th

Isn't it also obvious that if you have a floating helium balloon inside your car, when you brake the balloon will move forward inside the car, or when you accelerate the balloon will be pushed back?Isn't it also obvious that if your friend has three identical boxes with one of them containing a prize, you choose one box and he opens it revealing that the prize is not inside it and he tells you that you have one last chance to choose, then it doesn't matter if you keep your current choice or switch to the la

Bad example. Most people on a plane do not have piloting skills and frankly, they ought to be afraid of jumping into the pilot seat as should everyone else in the plane. Your example would be a more accurate analogy if being bad at math caused you to be more afraid of someone else doing the math for you.

Posts that claim to be "first" but aren't usually are in the "subitizing range" [wikipedia.org] (you see, I not only did read the fscking summary but also borrowed a link from it).

These people actually have the much feared Reverse Math Anxiety Syndrome (RMAS). People with RMAS suck at dealing with numbers up to four, but are very good with numbers from five upwards. Have you ever seen the 137th post claiming to be first?

Oh my god! That calc test on surface integrals is scaring me! How many days do I have until I have to take it? Let's see, one, two, four? Shit, shit! Let's start over. One, two, three, where was I? Oh god, how did I make it this far? Was this all some sort of ruse to make me feel good about myself? Has my whole life so far been a lie? How can I major in CS if I can't even count! If only I had learned that I was terribly afraid of math all those years ago....I think there is only one way out of here: majoring in education or running for office. Or is that two? Dammit, there we go again!

Just an anecdote but oddly enough most of the people I know that have gone on to high level math (>>Calc 3) tend not to be terribly good at doing basic math in their heads. It could be just my imagination or it could be that they rely much more on calculators/computers to do most of the actual calculations for them but it would be interesting to see a study on it. Perhaps study how anxiety affects basic math skills among those who are very advanced in mathematics.

I think it has a lot to do with the frequency of calculations. Most high order math doesn't require dealing with large numbers, but variables. So you don't get a lot of fiddling with actual calculations in your day to day life, other than maybe adding up bills (which you tend to estimate on anyway- you round things up or down for easy adding). I used to be able to take a square root to 4 significant figures in my head in just a few seconds. I still remember how, but trying to do so would take me a minu

Just an anecdote but oddly enough most of the people I know that have gone on to high level math (>>Calc 3) tend not to be terribly good at doing basic math in their heads.

Heh, I'm just the opposite. I'm very good at mental arithmetic, and I can multiply 4 digit numbers in my head usually faster than someone who reaches for a calculator, but I absolutely suck at math - especially trig (Calculus not so much). However I chalk it up to carelessness because I understand the concepts

Maybe these people are generally like my math prof during my university years. He was an absolute math genius. Yet calculation (ya know, the good ol' 2+2=4) was not his forte. Not because it was hard. Quite the opposite. It was boring. Or "trivial" as he loved to say. He hated trivial stuff. You could literally see how teaching entry level math was a veritable chore and outright torture to him. How come these idiots couldn't wrap their feeble brains around a simple concept like double integrals...

Maybe these people are generally like my math prof during my university
years. He was an absolute math genius.

I doubt it. If you compare with a true math genius such as Gauss [wikipedia.org], you'll find
that Gauss was incredibly interested in calculating things, ie obtaining an
actual number at the end that's correct.

I use and even sometimes teach factor analysis, item response theory (Rasch and multiparameter), structural equation modeling (okay, so most of those are flavors of the same thing), as well as a whole host of other statistical analyses. But as I prepare to go back to grad school for a PhD, and therefore need the GRE again, I'm struck--yet again--how absolute shit I am at arithmetic. Questions that require me to just manipulate variables around are no problem, but if they throw an actual value in there, and

Not always. That depends on whether the variable size represents the size of the array or a subset of the array. You get an exception if the array went out of bounds. If the data output looks screwy for an array subset, it's because the for loop is off by one.

Then it should blow when you're done stepping through the whole array. Or, if you're actually making sure something like this does not happen, you have your own tripwires in place to detect such routines that overstep their bounds.

My impression, through my own experience and people I have spoken to, is that maths is hard to learn because it is generally abstract. For example I get the general feeling that more people pass calculus when they are given an application that help provide a visual context to the skill, such as physics. This is probably the same reason why computers sometimes detract people from using them. The only difference is that we spend a huge amount of time and effort trying to make computers easy, though I am not sure the same can be said about mathematics.

Having sat through a number of maths classes, and lectures, I find that the people teaching the subject, often fail to appreciate that what they find easy is not necessarily the case for others. This means they don't show the necessary steps or fail to find techniques to facilitate the understanding. Sometimes its almost as if they want to make maths hard to learn. Of course people end up get anxious since they end up feeling stupid.

Although we talk about car analogies here, in order to make things easy to understand to the, I find the same can benefit maths. By trying to understand what the skill set of your audience is and adapting the teaching helps. For example the 'sum' sign looks hard until (if amongst computer people) you explain its just a 'for each' with addition and the 'pi' sign is a 'for each' with multiplication. In certain cases it is equivalent to the linguistic differences between English and Chinese, in that they both can talk about the same thing, but the way in which they do so is not the same.

"My impression, through my own experience and people I have spoken to, is that maths is hard to learn because it is generally abstract."

Something I blogged about 2 years ago:

So here I am thinking obsessively deep about what exactly that "biggest idea" should be in each of math and computer sci classes. And oddly I find that all the different math/compsci classes sort of get sucked into the same single, primary big idea in my head. My concern is that it's such a big idea that it can't fit into a single class, or really into the sequence of subjects already mapped out. Or that it will be comprehensible at the level of incoming students...

For today let's say it's this: Abstraction. Getting comfortable with it. Getting proficient with it. Knowing deeply what it implies (Getting rid of details. Panning out just the key big-league concept that you need to apply.) Being able to recognize that any knowledge domain will have a bunch of different abstraction levels, and being able to pick the right one you want to be working at. And being comfortable with forgetting everything else as long as yourk work lasts.

To summarize, I argue this: The whole point of a math class is to be abstract. If it's not abstract, then it's not math. If you didn't need to practice your abstraction skills, then you wouldn't need any math classes.

One difference I've noticed is people who are good at math tend to look at algebra in terms of pictures, or abstract chunks, whereas people who are not just get confused.

For example, a person good at math will see 3x+7y^2 +5 = 3x +7y^2 + c to be as simple as A+5 = A +c. They can group the complex group into a single piece in their mind. Or they can easily 'flip the chalkboard' around in the mind and realize that 7y = x is the same as x = 7y. If there is one thing that distinguishes a person who is goo

As an educator myself, I have grappled with this problem. Shared vernacular is hard to find. Just look at your own example: you used "for each" assuming that someone would understand what that meant. I have spent many hours trying to explain the concept of a for loop to very smart Chemical Engineering students, some never get it. I suppose we could conclude I was a bad teacher unless we consider that no course that I have heard of has 100% pass rate. There is a lot of active cognitive research into the

As a part-time music teacher currently doing a maths degree, it is strikingly obvious that most of my lecturers are utterly clueless about basic pedagogy. Some of their lecture techniques are downright harmful. The classic is issuing notes, but with blanks left in "so you have to pay attention". Result: lecturer flies through material and nobody pays him any attention while they try to find and copy down the blanks. Grrr.

The experiment sounds more like it highlights performance anxiety. Perhaps it's just me, but I don't equate simple "counting" with Math. Once you start doing something with the number you've counted, then it's Math.

Math anxiety is turning out to be a much more complicated phenomena than one might thing. For example, there also was a very interesting study by Sian Beilock at the University of Chichago. Beilock showed that young girls who were exposed to female elementary school teachers were much more likely to develop math anxiety themselves than those not exposed to such teachers. See http://hpl.uchicago.edu/Publications/PNAS_2010.pdf [uchicago.edu]. The exact consequences of Beilock's study are not clear. But combined with the study above, it seems to suggest that we need to do a better job with elementary school teachers. We need to either get rid of the school teachers with math anxiety or get rid of their math anxiety problems. Possibly some combination of both approaches may be in order: Improve the mathematical confidence of elementary school teachers whom we can effect and get rid of those we can't.

This is the first time on Slashdot that I'll that say there's a legitimate call for "correlation is not causation". The claim in the article is that "anxiety about mathematics can adversely affect tasks as simple as basic counting". But the reported data is simply that "math anxious individuals, relative to their non-math anxious peers, demonstrated a deficit in the counting range (five to nine)..."

I don't see any support for the hypothesis that math anxiety "affects" or "impacts" (per the article) basic math tasks. I think an equally-well supported hypothesis is that people who suck at counting to 5 wind up developing math anxiety.

To test their hypothesis, they need to take equally-skilled people and somehow make an experimental group anxious about the upcoming task (or something). I don't see that happening here. Frankly, I'm highly skeptical of this whole "math anxiety" postulate. I think we've got to accept the fact that for some people, even basic arithmetic is monumentally difficult, and not blame it on their "feelings" towards the task.

Anecdotally, I've seen people who did not start out with math anxiety but developed that later and observed a decline in counting skills. For example, my sister jokes that she forgot how to count after taking calculus. I'd say there's a pretty good chance that this really is causal, but of course further studies would be required to confirm that.

You are correct to state that this study does not prove causation, but you have to also take into consideration that this study does not exist in isolation. There is plenty of evidence to support the idea that anxiety about a task leads to a decreased aptitude at performing that task. Causation can be implied, but it can also be the case that there is causation in both directions: feedback that an individual is a poor performer at math reinforces the anxiety, which in turn causes the poor performance, resul

The idea that some people have a hard time with math is nothing new, but understanding what makes it difficult is important. If math anxiety affects people at such a basic level, addressing their anxiety could create a huge improvement. It would be interesting if we learn enough about how people learn that some day average math skills means a strong grasp of algebra and calculus without needing a calculator.

I've always had trouble with math, not so much understanding it but actually doing it. It got worse over the years, not just with harder math, but any math. Eventually I could tell I was actually having anxiety attacks when asked simple math questions. Now days these anxiety attacks are actually bad enough to trigger my flight-or-fight response. It's overwhelming and hard to describe, but if I don't focus entirely on calming down, it feels like I will 'lose control'. At this point the problem makes itself worse - I can be asked something I KNOW how to solve but I end up having to concentrate so hard on self control that I can't even take time to think about the problem I was asked. Not being able to think about the problem means I can't answer it, which makes the anxiety worse, which makes it even more impossible to stop and think about the math itself.

It's been pretty crippling, both socially and in work. I do everything I can to avoid situations that will be problematic. I simply stone wall anyone who tosses math at me, shutting down with simple 'no's and 'I can't's, leading them to assume I'm unintelligent and/or uneducated - an assumption I let them have because it's easier than trying to explain what's really going on.

I've never encountered anyone who even remotely understood, so I thought it was just me having an odd, unfortunate personality quirk. I mean nerds and anxiety go hand in hand right?

I happen to be one of these people, so I have some knowledge about the subject. Although I cannot speak for everyone, in my cause there was a very strong correlation between my fear of math (or my lack of math ability) and my performance. At a younger age (elementary school) I simply found math to be non-practical, and therefore ignored it(which is to say I did the bare minimum to get by in class). Once I did this however, by the time I got to highschool, I had severely fallen behind in math all around. My first and only class I failed was algebra, which I retook and finally passed with a C. To me, it was such an abstract thing that it seemed pointless in its difficulty. I should qualify that in all other subjects I excelled, including things like networking (boolean functions and binary, that I saw had practical benifit, I could do in my head no problem) Now, after serving in the military, and going back to college, it has been over 7 years since I had a college level math course, and still struggle, but I have found something that helps me tremendously. Finding practical applications that require whatever level of math I'm studying. My main tool for this at the moment, however bizarre this may sound, is building things in Garry's Mod, via the Wire Mod tool. It requires some very complicated mathmatical procedures to do something such as build a 10 cyclinder engine wiring to fire off in the correct sequence at high speed. In short, I believe it is a matter of learning types, I am a visual/kinetic learner, and need some substantial problem to wrap my head around and things have slowly (not without hard work) falling into place for me, and I'm sure I'm not the only one in a similar situation.

I wonder how much better they would perform if each correct response was earning them $50. Some people just won't follow even the most basic kind of instructions unless they are strongly and personally motivated.

The schools lost the ability to teach mathematics properly a couple of decades ago, starting with the "new math" in grade school and the "dumbing down" of math in high school.

Grading to the curve just sealed the deal. But like a bad TV infomercial - BUT WAIT! THERE'S MORE! By insisting that students solve all problems using calculators, students lost the ability to guestimate what range an answer should be i

Well, I've seen core bits that are on the high side of $250 each... but even then, just make a fixture that lets you stack them in a 10x10 configuration (think like a pool ball rack, but square), 10 x, you're done.

Or (again, assuming they're large bites, just lay out 50 side by side, put a couple of heavy blocks on either side, remove the bits, lay out another 50... it's not like you have to count the individual bits after the first batch of 50.

If a single bit is 250 bucks, you won't have THAT many customers that order a thousand at once. So having a person count thousands once in a blue moon works out. I was talking about mass produced trash.

Because otherwise, if you're going to count them, you'll get somebody (who, me?) who will come up behind you when you're going "656, 657, 658" and start counting "227, 228, 229, 765, 23, 11-teen,... hmmm, do you need any help?"

Ah, there's always one of those... in my garage, he's known as "the one who's about to get punched in the balls.";)

Hey, maybe those people are "anxious" about math because they're the ones that never did their math homework!

Maybe they were yelled at and threatened with violence when doing their math homework. Which made them distraught and unable to perform mathematically, which led to bad grades, which led to more yelling.

I know you'll dismiss that, since you're obviously devoid of empathy and compassion, but I thought I'd try to enlighten you anyway.

Maybe they were yelled at and threatened with violence when doing their sex ed. homework. Which made them distraught and unable to perform sexually, which led to bad sex, which led to more masterbating.

I know you'll dismiss that, since you're obviously devoid of empathy and compassion, but I thought I'd try to enlighten you anyway.

No I'm more of a results oriented person who believes that dwelling on the past is not constructive to future progress. The past exists to be learned from, not lived in. My own past is full of very real nightmares and ghosts, things have happened to me that make everyone who finds out gasp in amazement. The key to survival is getting over it, not using it a

Nothing helps you get over an anxiety problem like people telling you you're just lazy, let me tell you. You're just not working hard enough, stupid! Only an hour or two (or three) on your math homework? And you still haven't made any progress? You'll sit there all night until you miraculously figure it all out, dummy!

And every time you look down at that sheet you break into a cold sweat. You get a head full of fog, and every stab at every problem is like groping around blindly. You desperately flip through your notes or pour over the text book, both of which are like trying to read Cyrillic. And all the while, everyone else in the class blazes through the material, leaving you far behind. It's because you're not trying hard enough. Work harder, moron.

Psychologists might like the answer to be "Therapy"; but, even if they explicitly say so, I doubt it'll make much difference.

Basic anti-anxiety techniques can easily be administered by people much cheaper than psychologists(generic social workers, pretty much any teacher or aide with a little training) and there is a collection of anti-anxiety drugs with fairly favorable safety profiles that can be handed out by anybody who can write a prescription(which, if the experience with things like Ritalin is any

I've often wondered what would happen if you took a standard school intake class, gave them a short all-purpose test, told them they'd all passed with 95%+, and spent the rest of the year treating them like geniuses. To this day, I'm convinced that I am no smarter than my classmates were, but because I read books I was "the smart one" and hence I did end up doing better.